University of Notre Dame
Summer Diet Optimization by Beaver
Author(s): Gary E. Belovsky
Source: The American Midland Naturalist, Vol. 111, No. 2 (Apr., 1984), pp. 209-222
Published by: University of Notre Dame
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The American Midland Naturalist
Published Quarterly by The University of Notre Damne, Notre Dame, Indiana
Vol. 111 APRIL, 1984 No. 2
Summer Diet Optimization by Beaver
GARY E. BELOVSKY
School of Natural Resources, University of Michigan, Ann Arbor, 48109
ABSTRACT: Foraging data collected for beaver (Castor canadensis) at Isle Royale Na-
tional Park, Michigan, during the summer of 1973 provided basic natural history infor-
mation pertaining to diet, food preferences, rates of consumption and activity cycle.
Beaver foraging was consistent with a linear programming model of herbivore optimal
foraging. The model was used to predict beaver diet, the maximum distance a beaver
foraged from its pond, and the manner in which the minimum and maximum
diameters of beaver-cut woody vegetation changed with distance from the pond.
INTRODUCTION
Although many investigators have studied beaver (Castor canadensis), few quan-
titative data have been collected on food preferences and the basis for observed
preference (see Jenkins and Busher, 1979, for review). Beaver appear to change
preferences of both the species and diameters of plants they cut with increasing distance
from their pond Uenkins, 1975, 1978, 1979, 1980) and Jenkins (1980) points out that
this behavior might be explained by contingency models of optimal foraging
(Schoener, 1971; Pyke et al., 1977) and "central place foraging" [extension of con-
tingency foraging models to species that return, like the beaver, to a nest or "home"
(Schoener, 1979; Orians and Pearson, 1979)].
In this paper, preference for certain plant species exhibited by beaver and the
diverse mixture of plant foods in their summer diet will be examined to determine
whether they can be predicted using a quantitative optimal foraging model, a linear
programming model of optimal foraging developed specifically for herbivores (Belov-
sky, 1978). Finally, this herbivore foraging model is modified to include "central place
foraging" to account for beaver plant choice with increasing distance from the pond.
The model is applied, with limited data, to the foraging of beaver at one site; however,
the results indicate that the model might be of value to the study of beaver at other sites
and in other seasons.
STUDY AREA
Data were collected at three sites (two ponds and Lake Superior) in a forest at Isle
Royale National Park, Michigan. Isle Royale is a 520 km2 archipelago in Lake
Superior, 28 km from the nearest mainland. The upland forest surrounding all the sites
is dominated by Betula allegheniensis, but the forest canopy in the lowlands immediately
surrounding the two pond sites is primarily composed of Thuja occidentalis and Picea sp.
These forests are more fully described by Belovsky and Jordan (1978).
The two pond sites are located on Grace and Washington creeks. The third site is
Washington Harbor on Lake Superior. The Grace Creek pond is 3.5 ha and the
Washington Creek pond 1.5 ha; each of these sites maintained a single beaver family
and lodge. The Washington Harbor site is larger (20 ha) and contains several lodges.
All three sites contain aquatic macrophytes and are surrounded by abundant terrestrial
vegetation. The pond sites have soft bottoms but the lake site bottom is primarily sand
and gravel. These substrate differences lead to different aquatic macrophyte produc-
tion, species and species diversity.
METHODS
Data collected on beaver include: (1) use of woody vegetation in relation to
availability by species and by distance from the water's edge, and (2) diet and
behavioral observations. All measurements were made between 20 May and 31 August
1973.
209
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210 THE AMERICAN MIDLAND NATURALIST 111(2)
The use of woody vegetation by beaver was determined by randomly locating a
point on the water's edge of each site. Then, beginning with this point, transects
extending perpendicular from the shore were placed at 100-m intervals around the
shore. Each transect was 30 m long because beaver-cut plants were not common at
distances greater than 30 m. Each transect had three plots, 4 m in diam, placed along it
at 10, 20 and 30 m from the water's edge. A total of 21 transects (63 plots) were ex-
amined for the three sites. On each plot, the number of beaver-cut and uncut woody
plants, taller than 20 cm, were counted, identified to species, and their diameters
measured. The cut plants were measured at the point of cutting, while diameters of un-
cut plants were measured at 20 cm above the ground, the mean height at which cutting
occurred. The cut plants were classified as freshly cut (current summer) or older, by
the color of the wood.
Diameters of 64 plants (16 each of Sorbus americana, Betula papyrifera, Acer spicatum
and B. alleghaniensis) were measured at 20 cm; all leaves, new growth of twigs and bark
were collected, dried and weighed. These data were collected for plants between 0.5
and 10 cm diam, the sizes most common around the shoreline, and plants were
sampled uniformly across the size range. Regressions were then constructed for stem
diameter vs. leaf, twig and bark biomass for an average of all woody plants and for each
of the four species. The regressions were used to estimate food and building material
acquired by beaver.
Detailed diet and behavioral observations were made at the Grace Creek pond over
five 24-hr periods duringJune-August 1973. This beaver family (two adults, two year-
lings, four kits) was accustomed to the presence of humans, because this was a main
research site for moose (Alces alces) (Belovsky and Jordan, 1978). An observer located
on their lodge was permitted a clear view of most of the pond, the shoreline and en-
trance to the lodge. From this location, the observer was able to record the beaver fami-
ly's feeding movements during 15-min periods, even at night by sound or flashlight.
This information was used to compute daily feeding time as the sum of all adults and
yearlings observed feeding in each 15-min period divided by the number of 15-min
periods in a day and the number of adult-yearling beaver (4) in the lodge. The number
of times and the duration of the periods that beaver engaged in either aquatic or ter-
restrial foraging were recorded. The ambient air temperature, water temperature (10
cm below surface) and the internal air temperature of the lodge were recorded at each
half-hour for correlation with beaver feeding activity.
RESULTS
Beaver were selective in feeding on woody plants, cutting species of plants in pro-
portions significantly greater or less than their relative availability (Table 1, x2 = 76.9,
TABLE 1. -Species composition of woody plants cut by beaver at Isle Royale National Park,
Michigan, and the percent availability of deciduous plants. Species composition of cut plants is
based upon the number of stems cut. Availability is the percentage of plants of each species
within 30 m of the pond, based upon cut and uncut stems. A X2 goodness of fit test is used to
compare the cut and available stems
% Cut %O Available Significance
Sample size (# plants) 215 796 (p< 0.05)
Acer rubrum 0.5 n.s.
A. saccharum 31.6 15.0 sig.
A. spicatum 2.8 3.5 n.s.
Alnus rugosa 41.9 37.4 n. s.
Betula alleghaniensis 4.2 1.4 sig.
B. papyrifera 1.9 6.3 sig.
Cornus stolonifera 0.5 2.6 n.s.
Corylus cornuta 0.9 5.3 sig.
Sorbus americana 14.9 20.1 n.s.
Others 0.9 8.3
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1984 BELOVSKY: BEAVER DIET OPTIMIZATION 211
p <0 05, df = 9). Beaver preferred (diet proportion significantly greater than available)
Acer saccharum and Betula alleghaniensis, were indiffernt to (diet proportion not
significantly different from available) Alnus rugosa, Acer spicatum, A. rubrum, Cornus
stolonifera and Sorbus americana, and avoided (diet proportion significantly less than
available) Betula-papyrifera, Corylus cornuta, Lonicera canadensis, Abies balsamifera, Thuja oc-
cidentalis, Picea sp. and Sambucus pubescens. Furthermore, beaver did not change their
preference for plant species with increasing distance from the water.
When woody vegetation occurred in all three plots along a transect, a highly signifi-
cant inverse relationship existed between distance (d) from the water and percentage of
plants cut (r = 0.48, % = 88.0 e?8d, N = 33, p C 0.01). This relationship indicated that
beaver limited their cutting away from water. Mean diameters of woody plants that
were cut by beaver were significantly larger than the diameters of woody plants that
were not cut (cut: 2.5 cm 1.5, N = 215; cut + uncut: 1.3 cm 0.9, N = 796, t= 10.0,
p < 0.05). No difference existed between the mean diameters of woody plants cut iat the
different distances from water, but the smallest and largest 10% of cut-diameters were
different. The largest diameters of woody plants cut (10 m: 5.7 cm+ 2.1, N = 10; 20 m:
5.4 cm + 0.4, N = 6; 30 m: 3.8 cm, N = 2) decreased with increasing distance (r2 = 1.0,
Spearman rank correlation, p < 0.05). The smallest diameters of woody plants cut (10
m: 0.6 cm + 0.2, N = 10; 20 m: 1.0 cm t 0.2, N = 6; 30 m: 1.4 cm, N = 2) appeared to
increase with increasing distance r2 = 1.0, Spearman rank correlation, p < 0.05).
Beaver fed 269 min/day with distinct feeding periods (Fig. la). Beaver activity can
be correlated with the thermal environment (Fig. ib). The main activity period
(1900-0700) occurred during the coolest ambient air temperatures. The activity peak
from 1300-1500 occurred when the water was cooler than the air, and no major
temperature difference existed between the lodge and the water; thus, it is thermally as
equitable to forage as it is to rest.
When the beaver were close to the observer (< 50 m), and their selection of food
could be observed, beaver at Grace Creek pond 82 min ate aquatic macrophytes
4.9% of the time (4 min). While feeding on aquatics, beaver averaged two dives/min
with two plants per dive. If the average aquatic plant weighed 1.3 g dry wt (Belovsky
and Jordan, 1978), beaver were averaging an intake of 69.0 g dry wt/day (0.049 X 269
min/day X 1.3 g/plant X 4 plants/min). The remainder of the feeding observations in-
volved the cutting, transporting and consuming of leaves of woody plants (95.1%, 82
min).
At Grace Creek pond, 0.48 woody plants/M2 were cut by beaver between 20 May
and 15 August (88 days) on 18 plots monitored regularly and on which plants cut by
beaver (108 cut) were marked. From mapping the pond and the 30 m of land surround-
ing the shore used by beaver (Belovsky and Jordan, 1978), beaver were found to use
approximately 21,313 m2 of terrestrial area surrounding the pond. From this and the
fact that four beaver (two adults, two yearlings) were cutting these plants, foraging
beaver averaged 29 plants cut/day. Deciduous plants have an average leaf biomass
equal to:
I = 3.4D17 (1),
N=64, r2= 0.83, p<0.05) where 1 is measured in g dry wt and D is the diameter of
the main stem, 20 cm above the ground. Computing the average leaf biomass for a
woody plant using all diameters of beaver-cut woody plants, a beaver had an average
leaf intake of 551 g dry wt/day (19.2 g times 29 plants/beaver/day). Both terrestrial and
aquatic consumption will be slight overestimates since a portion of the food will be sup-
plied to kits.
The time required by beaver to cut woody vegetation was not measured because no
beaver was observed cutting from start to finish. Limited information from other
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212 THE AMERICAN MIDLAND NATURALIST 111(2)
studies on the cutting time vs. diameter of the plant exists (Fig. 2), indicating a rela-
tionship:
L: = 0.63eO?24D (2)
(r2 = 0.94, N = 9, p < 0.05), where t, is the cutting time in minutes. A beaver requires
an average of 1.24 min to cut a plant, based upon observations of all diameters of
woody plants cut by beaver.
DISCUSSION
Belovsky (1978; in press a & b) constructed a linear program model of optimal
foraging by herbivores using constraints for digestive capacity, foraging time, energy
requirements and nutrient requirements. The model can be solved for either energy-
maximizing or feeding time-minimizing strategies given species and site-specific values
for each constraint. An energy maximizer presumably acquires more energy than can
presently be used, so that fat can be stored for use in future periods of food scarcity or
reproduction. A time minimizer reduces its energy intake through feeding to enable it
to devote more time to other activities (grooming, lodge construction, etc.) or to reduce
20-
00
uII 20- 4* AIR
D LODGE
0 WATER
a-
llJ
2400 1200 2400
TIME CST)
Fig. 1. - a. The percentage of daily beaver foraging activity observed at each hour over an
average summer day, based upon 84 (adult-yearling) beaver exit-returns to the lodge over 5
days. b. Average hourly air, water and internal lodge temperatures at Grace pond over 5 sum-
mer days
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1984 BELOVSKY: BEAVER DIET OPTIMIZATION 213
its exposure to predators and other deleterious factors in the environment (Belovsky,
1978).
A linear program model is composed of a set of constraint equations:
C > or c Eaixi
1
where C is a constraint value that either cannot be exceeded or must be exceeded, xi is
the quantity of food i eaten and ai converts the quantity of food i eaten into the con-
straint units. With the constraint equations, an objective function is solved either for
energy-maximization or time-minimization:
P= =bixi
1
where P is energy intake or feeding time, and bi converts the intake of food i into either
energy or time. Linear programming models can be solved graphically if two foods are
considered, or by the Simplex algorithm for n foods (Belovsky, 1978).
To evaluate beaver foraging behavior and the results presented above, a quan-
titative foraging model can be applied. To solve the linear programming model for a
cn ~ ~ ~ ~ t0 30.24D
w 300 |t =0.63e
O r 2 0.94
p I 0.05
LI 200
Q) 100
F*
0~~~~~~
D*
5 10 I5 20 25
DIAMETER -CM
Fig. 2.-The time a beaver took to cut a woody plant as a function of the plant's diameter.
The time-diameter data were taken from Warren (1927), Rue (1964) and Wilsson (1971)
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214 THE AMERICAN MIDLAND NATURALIST 111(2)
beaver foraging during summer Uune-August), four constraints are required
(digestive capacity, foraging time, energy requirements and nutrient requirements).
All parameter values are based upon an adult beaver weighing 15 kg. The model is set
up for two food plant types: aquatic macrophytes and deciduous leaves.
1. The beaver's digestive capacity depends upon the g wet wt capacity of the
caecum/upper colon and stomach, and the rate at which food passes through the
digestive tract. Both the stomach and caecum/upper colon are used as a continuous
flow system by herbivorous rodents to break down plant tissues (McBee, 1971). A
15-kg adult beaver has a full stomach capacity of 530 g wet wt (Grinnell et al., 1937),
where partially filled stomachs were estimated to the full value based upon the in-
vestigators' estimates of the fraction filled, and the size of the beaver was proportionally
scaled to a 15-kg individual. Herbivorous caecal digesters have a caecal/upper colon
capacity approximately 1.8 times the stomach capacity (Belovsky, in press a, b for
Microtus pennsylvanicus and Lepus americanus; McBee, 1971). Hoover and Clarke (1972)
report a much lower caecal/upper colon capacity (3.77% of body wt) for beaver.
However, by their admission, their techniques will underestimate capacity and their
largest value of 6.1 % provides a comparable value to my estimate of 1.8 times stomach
capacity. Therefore, a beaver has a digestive organ capacity (stomach plus caecum/up-
per colon) of approximately 1484 g wet wt of food.
No information on the passage rate of green foods through a beaver's digestive tract
is available. Currier et al. (1960) and Stephenson (vide Currier et al., 1960) report that
beaver require 60-72 hr to eliminate 95-100% of the chromic oxide added to a dry
pelleted grain ration; however, they do not provide the mean retention time, average
time for a food particle to traverse the gut. Furthermore, green vegetation should pass
more rapidly through the digestive tract than a dry pelleted ration or a twig diet. Data
are available on the passage of green foods through the nutria (Myocaster coypus),
another large (> 8 kg) aquatic herbivorous rodent. In nutria which are fed lettuce and
a marker of dyed oat kernels, the average passage time is 10.3 hr (recalculated from
Gill and Bieguszewski, 1960). Thus, the digestive tract empties 2.33 times/day.
Accordingly, using the passage rate for nutria and assuming that passage time is
similar for all green plant tissues, a beaver has a total digestive capacity of 3458 g wet
wt/day.
Digestive capacity also depends upon the rate at which different plant types fill the
organs (wet wt/dry wt). These parameters were measured by Belovsky and Jordan
(1978). Using these values, the digestive capacity constraint is:
3458 g wet> 4L + 20A (3),
where L is the beaver's g dry weight daily intake of leaves and A is the g dry wt daily in-
take of aquatic plants.
2. Theforaging time constraint depends upon the amount of time available to a beaver
each day for foraging and the rate at which beaver crop aquatic plants and deciduous
leaves. I suggested that available foraging time might best be obtained by some means
independent of observing the animal's behavior (Belovsky 1978). An optimization
model of maximum allowable daily feeding time based upon thermal balance may be
used (Belovsky, 1981a). This concept avoids any chance that observed foraging time is
linked to the cropping time for different foods. This precaution is not available for the
beaver model because insufficient thermal physiology data are available. Coles (1966),
however, in a laboratory study of beaver thermoregulation, demonstrated that beaver
summer activity is probably limited by excessive heat gain and loss in temperate areas.
Therefore, given the correlation of observed beaver activity with thermal conditions, I
assume that a beaver's observed feeding time (269 min/day) equals its maximum
allowable time. Furthermore, the beaver lodge (Fig. ib) may function as a constant
thermal environment: cool when the air is hot and warm during the cool nights.
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1984 BELOVSKY: BEAVER DIET OPTIMIZATION 215
One might argue that beaver can forage all night (the period of most equitable ther-
mal conditions), such that the maximum time would be approximately 720 min. The
observed daily feeding activity, however, is far less than the 720 min suggested by
Busher (1975); but peak activity did occur in the same period found by Busher
(1900-0700) and a second activity peak from 1300-1500 was also found. Little
nonfeeding related activity was observed, less than 10%, suggesting that inclusion of
other activities (dam repair, unexplained swimming, etc.) would not increase activity
time to approach Busher's (1975) estimates. Two explanations for this discrepancy may
be proposed. First, Busher's (1975) estimate includes spring and autumn observation
periods of less thermal stress, perhaps permitting more feeding. Second, beaver might
only forage for 269 min as time minimizers to avoid predatory risk. However, the latter
explanation might not result in a correlation between thermal conditions and when
they forage.
The rate for cropping aquatic plants is 0.19 min/g dry wt. When cropping
deciduous plants, beaver swim an average of 106 m to the edge of the pond and then
walk 16 m on land. On average, beaver swim 69 m/min and walk 28 m/min (Green,
1936). At Grace Creek pond, it is estimated that beaver halve their walking and swim-
ming speeds while hauling cut branches. No cut branch or stem larger than 2.5 cm
diam is hauled intact, but more than one smaller branch is carried. Using this informa-
tion and eqns. 1 and 2, the cropping rate for deciduous leaves (CD: min/g dry wt) is:
24D 3.4D17 106 m + d 1 0 for Dc2.5 cm
16.1 i9m/min 28 m/min1 1.20 for D>2.5 cm
CD = (4),
3.4Dl 7 g dry wt
where 3.4D' 7/16.1 is the scaling factor for additional trips and cutting required for
plants with diameters different from 2.5 cm, d is the distance (m) from the pond, 3 is
the equivalent number of trips given the slower speed of transport, and 1.20 is the time
(min) required to cut a 2.5-cm branch from a larger plant. Averaging eqn. 4 over all
observed D and d values, the cropping rate for leaves is 0.49 min/g dry wt. Therefore,
on average, the feeding time constraint equals:
269 min 2 0.49L + 0.19A (5).
3. A beaver's energy requirement is estimated from the standard body weight-
metabolism relationship for mammals (Kleiber, 1961; Hemmingsen, 1960), increased
by 12 % because beaver are known to have a basal metabolism 12 % greater than the
average mammalian estimate (Coles, 1966). Furthermore, it is assumed that a beaver
requires twice its basal needs to satisfy additional energy expenditures for minimum
growth, winter fat storage and reproduction. Therefore, an adult beaver (15 kg) re-
quires on average 1213 kcal/day.
Information on the net energy content of plants eaten and the energetic expen-
diture for cropping by beaver is needed also. Belovsky and Jordan (1978) presented
gross energy values of 4.2 kcal/g dry wt for deciduous leaves and 4.1 kcal/g dry wt for
aquatic plants. Using data on the beaver's ability to digest different plant components
(protein, fat, NFE, cellulose) and rations (Novakowski, 1967; Cowan et al., 1957; Cur-
rier et al., 1960), the dry matter digestibility for a beaver is estimated to be 68% for
deciduous leaves and 80 % for aquatic macrophytes.
Schmidt-Nielsen (1972) found that the cost of swimming to a mammal is the same
as running; using Schmidt-Nielsens' data on energetic cost of running vs. body size, a
beaver expends approximately 0.02 kcal/m or 0.04 kcal/m in a foraging round-trip.
Brody (1945) found that farm draft animals are approximately 35% efficient in carry-
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216 THE AMERICAN MIDLAND NATURALIST 111(2)
ing a load, and a unit of work costs the animal 0.00234 kcal/kg-m or 6.7X0-6 kcal/kg-
m for actual energetic cost. The weight hauled by a beaver depends upon the leaf and
stem or twig weights. The stem-twig weight (T: g dry wt) equals:
T= 12.1D28 (6).,
(r2 = 0.81, N = 64, pC0.05). Usingeqns. 6 and 1 andincreasingdryweightbyamulti-
ple of two for stems-twigs and four for leaves to compute wet weight (Belovsky, 198 ib),
the average stem transported weighs 379 g wet weight. The energetic cost of transpor-
ting woody foods (Et: kcal/g dry wt of leaves) is estimated as:
316.D (106 m + d)[0.04 + (6.7Xl0O6) (379 g wet wt)]
E 16.1 (7),
= ~~~~~3.4D17 77
Averaging eqn. 7 over all D and d values observed, E, equals 0.30 kcal/g dry wt and the
energy requirement constraint equals:
1213 kcal/day < [(4.2 kcal/g dry wt)(0.68) - 0.30 kcal/g dry wt]L
+ (4.1 kcal/g dry wt)(0.80)A (8).
4. Nutrient requirements of beaver were not measured because captive beaver were not
kept and feces and urine could not be collected in the water where beaver deposit them.
Isle Royale is known to be a potentially sodium-poor habitat for beaver (Botkin et al.,
1973), and two other Isle Royale herbivores (Alces alces amd Lepus americanus) are
limited in their foraging by sodium intake (Belovsky, 1978, in press b). However,
Schmidt-Nielsen and O'Dell (1961) demonstrate that beaver urine is very low in solutes
suggesting that beaver might have low sodium excretory losses.
The linear program model could be constructed without nutrient constraints and
solved for time minimization and energy maximization. If one of the two alternative
strategies predicts the observed beaver diet, nutrients can be discounted as an impor-
tant foraging constraint for Grace pond beaver. However, if neither strategy could be
demonstrated, then either other constraints might be operating, for which sodium is a
likely alternative, or beaver might not be employing either of the two foraging
strategies (Lewontin, 1979).
The modelfor beaver diet selection can be solved using eqns. 3, 5 and 8. The constraint
equations are plotted in Figure 3 and the alternative strategies are examined. Beaver
appear to be energy maximizers (Table 2) because the time-minimizing diet is
significantly different from the observed diet on the basis of feeding observations con-
verted into food items (leaves, aquatic plants) (N = 82, X2 = 15.85, pcO.005) and did
not differ from the energy-maximizing diet (X2 = 0.001, p c 0.95). Beaver do not ap-
pear to have any nutrient constraints, especially sodium, probably due to sufficient in-
take from aquatic plants during summer (Botkin et al., 1973) and bark at other times of
the year (Likens and Bormann, 1970). Also, beaver do not appear to consume certain
planis for sodium, as Isle Royale moose do with aquatics (Belovsky, 1978).
As pointed out above, one might argue that the 269 min/day for feeding is less than
the maximum because of risk considerations. If this is true, one cannot claim that
beaver are energy maximizers in their overall foraging strategy, but one can still point
out that given the foraging time, beaver maximize their energy intake. Given the close
fit between the model and observed behavior, even with limited data for the model's
parameters, the diet optimization approach appears potentially useful.
The model can be solved to determine how the diameters of woody plants selected by beaver change
with distance from the pond. Belovsky (198 ib) demonstrates that herbivores may be
limited in their selection of plants by quality (digestibility) and quantity (cropping
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1984 BELOVSKY: BEAVER DIET OPTIMIZATION 217
rate). Net energy content or digestibility of deciduous plants is not important for deter-
mining a beaver's movement away from the pond, because a beaver requires only 1.9
kcal/g dry wt to satisfy its energy requirements with the digestive capacity available
after consuming aquatic vegetation [(1213 kcal required-223 kcal from
aquatics)/(3458- g wet wt of digestive organ - 1360 g wet wt intake of aquatics)/(4 g
wet/g dry for leaves)] or a 52% digestibility for leaves. In addition, using eqn. 7
summed over all D, the beaver are able to forage 253 m from the pond, a distance far
greater than observed.
On the other hand, the cropping rate constraint requires a beaver to acquire 3.87
kcal/min [(1213 kcal required-223 kcal from aquatics)/(269 min/day-13 min/day
spent cropping aquatics)] after intake of the energy-maximizing quantity of aquatic
vegetation. Combining the caloric value for leaves (2.86 kcal/g-dry wt) with eqns. 4
1500
FEEDING TIME
1000
500-
a\
METABOLISM
_ DIGESTI I
CAPAiT ENERGY MAXIMIZED
TIME MINIIM IZE D
500 1000
LEAVES (G-DRY WT)
Fig. 3. -The linear program constraints for a beaver. The striped area represents diet com-
binations capable of satisfying a beaver's energy requirements. The predicted time-minimizing
and energy-maximizing feeding strategies are labelled
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218 THE AMERICAN MIDLAND NATURALIST 111(2)
and 7 summed over all D and simplifying, the following inequalities must be satisfied
by a beaver:
3.87 kcal/min ? 2.58-2.65X10-3d
0. 19e024D +0.007d + 0.29 for DC2.5 cm
D17 0.37 for D>2.5 cm
Using the above inequality, the minimum and maximum diameters predicted to be
cut by a beaver at Grace pond are presented in Figure 4, along with the kcal/min
isoclines for values greater than 3.87 kcal/min. These solutions confirm the general
size-distance relationship found by Jenkins (1 980); i.e., maximum size declines with
distance while minimum size increases. The minimum observed diameters of woody
plants cut at 10, 20 and 30 m are predicted (Fig. 4: r2 = 0.98, p C 0.06). The maximum
sizes cut are far less than those predicted at 10 and 20 m; however at 30 m the observed
and predicted values were in closer agreement. This lack of agreement may be due to
the absence of woody plants with diameters large enough to limit beaver cutting at 10
and 20 m, but at 30 m available stem diameters are large enough that beaver must be
selective.
At Grace Creek, the maximum distance from the pond at which woody plants are
cut is predicted to be 40 m and the observed maximum distance is 48 m. Both the
minimum-maximum diameters selected and the maximum distance of cutting by
beaver from water should change from site to site. These changes in diet selection by
beaver with energy costs and transport time are as expected from "central place forag-
ing" theory (Jenkins, 1980). This behavior might also arise from predatory risk. The fit
to the quantitative foraging model and the changes in diameters selected by beaver,
however, indicate that the energetic and time considerations for foraging may be more
appropriate than the predation hypothesis.
The model can be solved to determine whether beaver preferences for woody plant species depend
upon leaf biomass of each species obtained/minute spent cropping. The measured g
dry weight of leaves available per plant vs. diameter is used to calculate regressions for
several plant species. Using the above regressions, eqn. 4 solved for a mean distance
travelled of 16 m, and the distributions of available diameters by species, the g dry
weight of leaves removed/minute cropping for each of four species is computed (Table
3). These values are compared with the percentage of each species used by beaver
(Table 3: # cut X 100/# available), indicating that plants may be selected for their
weight of leaves per unit time in harvesting (r2 = 0.93, p < 0.05).
It is interesting that Sorbus americana is not preferred by beaver since this species is
highly preferred by moose in summer and winter (Belovsky and Jordan, 1978; Belov-
sky, 1981b). Betula alleghaniensis is preferred by beaver but not by moose in summer
(Belovsky and Jordan, 1978), and preferred by both in winter (Belovsky, 1981b).
Other than these two exceptions, beaver and moose preferences for deciduous species
are the same. The differences may be explained in part by the foraging behavior of
beaver and moose. Moose crop woody plants, like most herbivores, by items (leaves or
TABLE 2. -Diets of beaver predicted by the linear program model are compared with the
observed diet of beaver at Grace Creek pond
Time minimization Energy maximization Observed
g dry wt % g dry wt % g dry wt %
Deciduous leaves 339 76 523 88 556 89
Aquatic plants 105 24 68 12 69 11
Total 444 591 625
Energy (kcal) 1213 1562 1647
Time (min) 186 2699 286
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1984 BELOVSKY: BEAVER DIET OPTIMIZATION 219
twigs), incurring a small cropping time expenditure per item. On the other hand,
beaver crop woody vegetation by the plan't, subsequently cropping leaves, twigs and
bark. This leads to an initially large cropping time expenditure by beaver. Therefore,
beaver preference might be related to the quantity of items available per plant cut, a
consideration not faced by most herbivores that would be concerned with items per
unit area and item size (Belovsky, 1981b).
The linear program model of beaver foraging can be examined for sensitivity to constraint
changes. The feeding time and digestive capacity constraints are the only constraints
operative in the energy-maximized solution. Each constraint can be varied (both in-
creased and decreased) to determine how large a change is needed to vary leaf intake by
10%. If daily feeding time is increased by more than 26% or decreased by 10%, leaf
intake will vary by 10 %T. Digestive capacity must be increased by 69 % or decreased by
30-
X
25-
E
20 - 3.87
w
1 5-
UI-I
0
wI
2.5- 5.0 __
A
5I
0 20 30 40 50
DISTANCE FROM POND - m
Fig. 4.-Predicted maximum and minimum diameters of woody plants that a Grace pond
beaver can cut at varying distances from the water. The solid line refers to the estimated beaver
requirement of 3.87 kcal/min, while the dashed line refers to minimum-maximum diameters if a
beaver's energy/time food intake requirements are 5 kcal/min. Triangles represent the observed
minimum-maximum diameters cut by beaver at varying distances from Grace pond
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All use subject to JSTOR Terms and Conditions
220 THE AMERICAN MIDLAND NATURALIST 111(2)
34% to cause leaf intake to vary by 10%. In terms of relative diet change, the above
constraint variations lead to diets of 72-100 % leaves. Finally, if a beaver's energy re-
quirements are increased by 38%, the energy-maximizing diet can satisfy only basic
requirements. These results indicate that the model is potentially insensitive to realistic
errors in the constraint values, and beaver diets at other Isle Royale sites and temperate
areas may not be influenced by changes in these constraints.
Parameter values converting food intakes into constraint values, however, may be
important. Bulk (wet/dry weights) values for different foods are probably not sources of
variation, because they are likely not to vary by more than 5-10%. Cropping times,
however, can change dramatically with abundance of vegetation and distance travelled
to the water's edge. Cropping times of aquatic and terrestrial herbaceous plants (the
latter not important at Grace Creek pond) should be particularly susceptible to vegeta-
tion abundance; however, woody plant cropping rates should depend upon cutting
time. Svendsen (1980) found that the proportion of woody vegetation in beaver diets
did not change very much even though woody vegetation abundance changed by a
large amount. From the model, the cropping rate of aquatic plants must increase by
158% to decrease woody vegetation consumption by 10%, while woody vegetation
consumption is insensitive to declines in aquatic cropping rates. On the other hand,
woody vegetation cropping rates must increase by 11 % to decrease woody vegetation
consumption by 10 %, and decrease by 9 % to increase consumption by 10%.
Therefore, with the combination of abundant herbs in adjacent meadows with woody
vegetation, a beaver might increase terrestrial foraging, but changes in aquatic plant
abundance have little effect on terrestrial diet.
CONCLUSION
Beaver at an Isle Royale pond appear to select their diet in a manner consistent
with an energy-maximizing solution to a linear programming model (Belovsky, 1978).
This model was originally developed for an examination of moose diet optimization
(Belovsky, 1978). With slight modifications for a beaver's "central place" foraging, the
model predicts not only the beaver's diet but also its selection of woody plant diameters,
species and distance foraged from the pond. Cropping rates of foods were potentially
the most important factor that could lead to diet changes. The successful predictions of
the model given limited data indicate that this approach may merit further considera-
tion for beaver foraging.
Acknowledgments. - I thank J. Cannon, K. Hay, D. Johnson, D. Pletcher and J. B. Slade for
their help in collecting the data, and the personnel of Isle Royale National Park for their help. I
thank T. W. Schoener, S. H. Jenkins, S. L. Lima, J. B. Slade and three reviewers for reading
critically drafts of this paper and supplying helpful comments. The work was supported by NSF
grant DEB-78-02069 AO1 to the author and T. W. Schoener, and grants to the author from the
Environmental Education Fund, and the Harvard Society of Fellows and the Richmond Society
of Harvard University.
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TABLE 3. -Prediction of food intake rate by a beaver cutting an average plant of four species
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Expected gain
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Betula papyrifera 8.0 0.6
Sorbus americana 20.0 1.3
Acer spicatum 21.0 0.8
Betula alleghaniensis 82.0 2.5
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1984 BELOVSKY: BEAVER DIET OPTIMIZATION 221
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SUBMITTED 17 NOVEMBER 1982 ACCEPTED 22JUNE 1983
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